Accuracy measures for a forecast model

Returns range of summary measures of the forecast accuracy. If x is
provided, the function measures test set forecast accuracy
based on x-f. If x is not provided, the function only produces
training set accuracy measures of the forecasts based on
f["x"]-fitted(f). All measures are defined and discussed in Hyndman
and Koehler (2006).

Arguments

f

An object of class “forecast”, or a numerical vector
containing forecasts. It will also work with Arima, ets and
lm objects if x is omitted -- in which case training set accuracy
measures are returned.

...

Additional arguments depending on the specific method.

x

An optional numerical vector containing actual values of the same
length as object, or a time series overlapping with the times of f.

test

Indicator of which elements of x and f to test. If
test is NULL, all elements are used. Otherwise test is a
numeric vector containing the indices of the elements to use in the test.

d

An integer indicating the number of lag-1 differences to be used
for the denominator in MASE calculation. Default value is 1 for non-seasonal
series and 0 for seasonal series.

D

An integer indicating the number of seasonal differences to be used
for the denominator in MASE calculation. Default value is 0 for non-seasonal
series and 1 for seasonal series.

Value

Matrix giving forecast accuracy measures.

Details

The measures calculated are:

ME: Mean Error

RMSE: Root Mean Squared Error

MAE: Mean Absolute Error

MPE: Mean Percentage Error

MAPE: Mean Absolute Percentage Error

MASE: Mean Absolute Scaled Error

ACF1: Autocorrelation of errors at lag 1.

By default, the MASE calculation is scaled using MAE of training set naive
forecasts for non-seasonal time series, training set seasonal naive forecasts
for seasonal time series and training set mean forecasts for non-time series data.
If f is a numerical vector rather than a forecast object, the MASE
will not be returned as the training data will not be available.

See Hyndman and Koehler (2006) and Hyndman and Athanasopoulos (2014, Section
2.5) for further details.